{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T14:56:25Z","timestamp":1740149785485,"version":"3.37.3"},"reference-count":35,"publisher":"MDPI AG","issue":"5","license":[{"start":{"date-parts":[[2019,5,19]],"date-time":"2019-05-19T00:00:00Z","timestamp":1558224000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"University Mediterranea of Reggio Calabria - Dept. of Law, Economics and Human Sciences","award":["grant number \"Decisions Lab 2019\/1\""]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"The subject of this paper is to analyse the Mathematical Principia of Economic 3D Black Holes in Roegenian economics. In detail, we study two main problems: (i) mathematical origin of economic 3D black holes; and (ii) entropy and internal political stability depending on national income and the total investment, for economic Reissner\u2013Nordstr\u00f6m (RN) 3D black hole. To solve these problems, it was necessary to jump from macroeconomic side to microeconomic side (a substantial approach as they are so different), to complete the thermodynamics\u2013economics dictionary with new entities, and to introduce the flow between two macroeconomic systems. The main contribution is about introducing and studying the Schwarzschild-type metric on an economic 4D system, together with Rindler coordinates, Einstein 4D partial differential equations (PDEs), and economic RN 3D black holes. In addition, we introduce some economic Ricci type flows or waves, for further research.<\/jats:p>","DOI":"10.3390\/e21050509","type":"journal-article","created":{"date-parts":[[2019,5,20]],"date-time":"2019-05-20T15:05:07Z","timestamp":1558364707000},"page":"509","source":"Crossref","is-referenced-by-count":0,"title":["Entropy of Reissner\u2013Nordstr\u00f6m 3D Black Hole in Roegenian Economics"],"prefix":"10.3390","volume":"21","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-7132-6900","authenticated-orcid":false,"given":"Constantin","family":"Udriste","sequence":"first","affiliation":[{"name":"Faculty of Applied Sciences, Department of Mathematics-Informatics, University Politehnica of Bucharest, Splaiul Independentei 313, Bucharest 060042, Romania"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3663-836X","authenticated-orcid":false,"given":"Massimiliano","family":"Ferrara","sequence":"additional","affiliation":[{"name":"Di.Gi.ES, University Mediterranea of Reggio Calabria, Seconda Torre, Loc. Feo di Vito, 89125 Reggio Calabria, Italy"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9160-9185","authenticated-orcid":false,"given":"Ionel","family":"Tevy","sequence":"additional","affiliation":[{"name":"Faculty of Applied Sciences, Department of Mathematics-Informatics, University Politehnica of Bucharest, Splaiul Independentei 313, Bucharest 060042, Romania"}]},{"given":"Dorel","family":"Zugravescu","sequence":"additional","affiliation":[{"name":"Institute of Geodynamics \u201cSabba S. Stefanescu\u201d, Romanian Academy, Dr. Gerota 19-21, Bucharest 020032, Romania"}]},{"given":"Florin","family":"Munteanu","sequence":"additional","affiliation":[{"name":"Institute of Geodynamics \u201cSabba S. Stefanescu\u201d, Romanian Academy, Dr. Gerota 19-21, Bucharest 020032, Romania"}]}],"member":"1968","published-online":{"date-parts":[[2019,5,19]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"1743","DOI":"10.1103\/PhysRev.119.1743","article-title":"Maximal extension of Schwarzschild metric","volume":"119","author":"Kruskal","year":"1960","journal-title":"Phys. Rev."},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Dabholkar, A., and Nampuri, S. (2012). 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